Gravity Waves and Black Holes

Transcription

1 Gravity Waves and Black Holes Mike Whybray Orwell Astronomical Society (Ipswich) 14 th March 2016

2 Overview Introduction to Special and General Relativity The nature of Black Holes What to expect when Black Holes collide Laser Interferometer Gravitational-Wave Observatory (LIGO) LIGO results announced on 11 th Feb 2016 What next?

3 Special Relativity Published in 1905 by Einstein Built on the following ideas: Relativity of motion ideas dating from Galileo and Newton Maxwell's equations of electrodynamics (1861) Michelson & Morley experiment (1887) 1 v 2 /c 2 Lorentz transformation (1892 to 1904) Poincaré (1902) suggests perhaps all physical laws should be invariant under Lorentz transformation

4 Special Relativity Assumes light travels at a constant velocity, whatever the velocity of the observer Treats Time as a 4 th dimension Spacetime Time is no longer a fixed/universal thing and simultaneity has no obvious meaning Mass increases with velocity: M = M 0 / (1 v 2 /c 2 ) Energy/Mass equivalence: E M 0 c 2 + 1/2 M 0 v 2

5 General Relativity Published in 1915 by Einstein Generalised his Special theory to include the effects of Gravity Asserts that Gravity and Acceleration are the same thing (Principle of Equivalence)

6 Implications of General Relativity Space [and hence spacetime] is no longer geometrically flat E.g. the Earth causes a local distortion: Radius of Earth calculated from its Area is given by r= A/4π But measure the radius directly and it would be 1.5mm longer than this!

7 Curved Spacetime Spacetime tells matter how to move; Matter tells spacetime how to curve. (John Wheeler)

8 Further Implications Time slows down in a gravitational field (and also as you move faster, as in Special Relativity)

9 Confirmations of General Relativity Advance of the perihelion of Mercury (1916) Deflection of starlight by the sun (1919) Redshift due to gravity (1925) Gravitational lensing (1979) Slowing of orbits of binary pulsars (1982) Frame dragging (2011)

10 Gravitational Waves Disturbances to spacetime travel at the speed of light PSR Hulse Taylor binary of two neutron stars (pulsars) Accurate timing studies show orbital decay matching predicted energy loss to gravitational waves

11 Black Hole 'Something so massive that even light cannot escape its gravity' Conjectured using Newtonian gravity by John Mitchell (1784) and Laplace (1796) Schwarzschild (1915) solved Einstein's GR equations for a non-rotating non-charged spherical mass: R s = 2GM/c 2 The Schwarzschild Radius is the size of the Event Horizon of a Black Hole

12 Black Hole sizes Mass compressed to become a Black Hole Mass (kg) Rs (m) Diameter 'Density' g/cm3 Moon 7.3E E mm 1.4E+31 Earth 6.0E E cm 2.0E+27 Jupiter 1.9E E m 2.0E+22 Sun 1Mʘ 2.0E E km 1.8E+16 Neutron Star 2.8E E km 9.3E+15 Black Hole 10Mʘ (Stellar BH) 2.0E E km 1.8E+14 Black Hole 30Mʘ (Stellar BH) 6.0E E km 2.0E+13 Black Hole 100Mʘ (Intermediate BH) 2.0E E km 1.8E+12 Black Hole 1E4Mʘ (Intermediate BH) 2.0E E AU 1.8E+08 Black Hole 1E6Mʘ (Intermediate BH) 2.0E E AU 1.8E+04 Black Hole 4.1E6Mʘ Sagittarius A* 8.2E E AU 1.1E+03 Black Hole 1E8Mʘ (Supermassive BH) 2.0E E AU 1.8 Black Hole 1E10Mʘ (Supermassive BH) 2.0E E LY Black Hole 4E10Mʘ Blazar S E E LY

13 Black Hole properties Black Holes are completely characterised by the parameters: Mass Charge Angular Momentum (spin) All astrophysical Black Holes are expected to have very little intrinsic charge Most Black Holes will have significant angular momentum a Kerr Black Hole

14 Kerr Black Holes A Black Hole with angular momentum Frame dragging creates a region called the Ergosphere in which space rotates so fast that it is impossible to remain stationary The Singularity becomes a Ring Singularity There is a maximum spin (Kerr parameter = 1)

15 Formation of Black Holes Big Bang could have formed Black Holes of any size including microscopic ones End of life of a star of original mass over about 20 solar masses Black Hole with mass in the range 1 to ~1000ʘ Growth of Intermediate and Supermassive Black Holes through accreting nearby gas, dust, stars, etc., and by mergers

16 Evaporation of Black Holes Hawking radiation Equivalent Mass Schwarzschild Radius Temperature Sun 3 km 1E-9 K Earth 9 mm 0.02 K Moon 0.1mm 1.7 K 1/10 Moon 0.01mm 17 K 1/100 Moon 1 μm 170 K 1/1000 Moon 0.1 μm 1700 K 1/2000 Moon 0.05 μm 3300 K 1/5000 Moon 0.02 μm 8400 K The Information Paradox - ongoing debate about destruction of 'physical' information

17 Mergers of Black Holes Simulations indicate the expected form of gravitational waves from Black Hole mergers: a 'chirp'

18 Detection of Gravitational Waves 1960: First attempts by Weber using resonant mass detectors 2000: Interferometer based detectors TAMA300, GEO600, LIGO 2015: Advanced LIGO, and Virgo

19 Hanford Advanced LIGO Livingston

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21 Advanced LIGO

22 First Gravitational Wave Detected! Date: 14 th Sept 2015 Time: 09:50:45 UTC Name: GW Arrival at Hanford 6.9ms later than at Livingston Peak strain of equal to about 1/10,000 width of a proton.

23 Interpretation of GW data

24 Simulation of GW type merger Video link here:

25 Location of GW 'Circle' defined by arrival time difference (6.9ms) Location on circle set by weaker constraints (amplitude, phase etc.) Masses determined by chirp 'frequency' then distance derived from luminosity/amplitude ~410Mpc (~1.3 Billion Light Years)

26 Consistency with General Relativity Inspiral models based on relativity match GW data Parameters for BH spin etc. inferred from early inspiral stage match those derived independently from late stage

27 A second detection? LVT Much weaker event false alarm probability about 0.4 per year If of astrophysical origin corresponds to another binary Black Hole merger Properties: M1 23ʘ (+18 / -5) M2 13ʘ (+4 / -5) Distance 1100 Mpc (+/- 500)

28 Expectations More similar detectors (Virgo, Kagra, maybe LIGO in India) Improvements to Signal/Noise Ratio Space based detectors e.g. LISA (Laser Interferometer Space Antenna) in ~2025 Sensitive over range Hz to 0.1Hz ->High redshift sources, and supermassive BHs

29 Credits and references Relativity Richard Feynman's lectures: Six not-so-easy pieces. Allen Lane The Penguin Press LIGO Various papers, images, video etc: including: Observation of Gravitational Waves from a Binary Black Hole Merger. B P Abbott et al. Physical Review Letters. 11 Jan 2016 Gravity Wave moving GIF: Orbit_times.png: P. Fraundorf

30 Questions?